Analysis of Rubber Roller Coating and Influence of Rubber Roller Characteristics on the Coating Thickness

: This paper has got the relationship between coating thickness and roller radius,speed, viscosity,elastic modulus,load,which is through the analysis of rubber roller’s coating flow mathematical model,and verify the elastic modulus and the load force on the coating thickness through the experimental methods. Experiments show that the coating thickness is inversely proportional to the elastic modulus and the load force.In conclusion, the diameter of the roller, the range of load imposed on the rubber roller, the hardness of rubber roller hardness, the suitable viscosity range and the speed limit must be taken into account during the design of the five rollers solvent-free coating system.


Introduction
Roll coating is now the most commonly used in coating industry.It's the methods that one or more rollers produce liquid film on the continuous operation of the medium format or something painted [1][2][3][4][5]. There are various forms of roll coating, but from the type of roll,they can be divided into two categories: rigid roll coating and the defornable roll coating. Rigid roll coating has been the focus of the study, either forward roll coating or reverse roll coating, which has always been the most frequently used in the coating industry. Relative to the rigid roll coating, the development of deformable roll coating relatively slow. rubber roll their own characteristics bring a lot of troubles to study mechanism on coating flow , and the deformation of rubber roller make coating flow more complicated. However, the emergence of rubber roller coating fill the lack of rigid roller coating , to avoid the impact of two rigid roller collide ,which has important significance on the coating industry.

the characteristics of roll coating
The general form of roller coating is made of rubber roller and rigid rollers, with two rollers pressed tightly together by external forces, as shown in Figure 1. Rigid roll is treated as a coating roll. When the film passes through the gap formed by rubber roller and rigid roller, the rotating coating roller brings up gel mucus in plastic tank and coats the plastic coating on the film to carry out the coating process. Compared to rigid rollers with fixed coating gap, the biggest difference of rubber rollers is that they have deformed coating gaps [6][7][8][9]. The speed of rubber roller coating can reach 360m/min; the applicable range of plastic mucus viscosity is from 0.01 to 5 Pa • s; the thickness of coating applied in wet coating ranges from 5 to 100 μm.
On one hand, rubber roller coating has its own advantages, compared with rigid roller coating; on the other hand, there are also some disadvantages. Its advantage are: (1) With a deformed coating gap, it can produce more stable and thinner coating; (2) Avoid the direct impact of two rollers; (3) Reduce or delay the emergence of defects, like coating stripes; (4) It can transfer adhesive mucus coating which has been measured [10]; (5) easy for maintenance and control, and less sensitive to mechanical tolerances; Its disadvantages are: As elastic properties of rubber roller elastic layer can be easily influenced by environmental changes, such as pressure, temperature of rubber layer, it can cause the changes in flow field of coating, thereby affecting the quality of coating.

the theoretical analysis of rubber roller coating
The mathematical model of rubber roller coating flow field is complex, because of it depends on deformability of the rubber roller. According to the different type of contact between rubber roller and rigid roller, roller coating can be divided into the positive space clearance roller coating and the negative space clearance roller coating [10][11], shown in Fig. 2. The gap of positive space clearance roller coating exists in between the two roller surfaces, but it in the embedded part between the two roller surfaces in the negative space clearance roller coating. These two types of rubber roller coating are the important parts of deformable coating models, but the rubber roller deformation type is different. The former is due to pressure field between two rolls which comes from high speed rotating, however, the latter is due to the deformation in the rigid roller surface because of the loading force.
Assuming the radius of rubber roller is R1, the radius of coating roller is R2, the center distance of two rollers is L0, and so we can judge: The positive space clearance rubber roller coating The negative space clearance rubber roller coating L0< R1 +R2 (2) Usually, the clearance between two rollers is assumed to 2H0, regardless it is the positive space clearance rubber roller coating or the negative space clearance rubber roller coating. The minimum clearance between two rollers is influenced by fluid pressure which comes from the slime in rubber roller elastic layer and the elasticrestoringforce of rubber layer.

Theoretical model of Rubber roll coating
The following illustrates the theoretical model of roller coating by the negative space clearance roller coating as the main research object.
In Fig. 3, in the forward rotation rubber roller coating, rubber back pressure roller and coated steel roller tightly connected by the load force F, the Rubber roller surface cause elastic deformation in steel roller surface, deformation length is D, the clearance between the two rollers is 2H0. Because of the deformation of the rubber roller, it is hard to forecast the deformation of the position, so the theoretical analysis with the free surface problems becomes more complicated. For steady, isothermal flow of incompressible liquid, the dimensionless Navier-Stokes equa-tions in divergence form with the corresponding boundary conditions are : Continuity equation: where for isotropic Newtonian liquids, Here μ and p denote the non-dimensional velocity and pressure fields respectively, and I is the unit dyadic; In the rubber roller coating, according to the changes in flow field and its own characteristics, the coating thickness can be approximated [12]: 0.4Es 0.6 Fw -0.3 (6) Here e is coating thickness, Es denotes elasticity number, Fw is load parameter Besides, elasticity number Es can be expressed: Here η is the viscosity of the fluid, which is assumed to be newtonian. E denotes the effective elastic modulus of the rubber materials, R is roll radius.
load parameter Fw can be expressed: Here W is Applied load. Substituting Then,coating thickness e can be obtained: From above，the conclusion can be drawn：Coating thickness is concerned with roll radius, roll speed, viscosity, elastic modulus and the load force. Rubber layer thickness has little effect on the coating thickness. Studies have shown that as long as half the width of the roll contact part is less than rubber thickness, the rubber thickness is extremely small effect [13][14].

the stability of rubber roller coating
Studies have shown that the rubber roll coating and the rigid roll coating both are prone to instability, especially in the forward coating,the performance is more significant,shown in Fig.4.So Ribbing coating defects are inevitable feature. In the coating process, we should minimize the appearance of coating stripes.In the study we can find ,in general conditions, the value of rubber roller speed increases more than 70%,it will prouce coating stripes.However,If we increase the width of two rolls contact surface, coating flow will flow back into a stable state [15].Besides，we can also reduce the speed or use a thinner flexible layer, it will make the wavelength of stripe becoming smaller [16].

Fig. 4 Ribbing coating defects
Usually in the study of the stability of Ribbing coating ,the standard of the general use is [17][18] :

N2
(11) Here r is radius of curvature of the meniscus ，N denotes dimensionless wave number of (rib) disturbance， x is stream wise cooridate in the direction from the gap to the free surface. C is capillary number(viscous/surface tension force ratio, C =μV/σ).
If the pressure gradient dp/dx> 0, the surface tension nakes the phenomenon of ribbing stability.

Influence of rubber roller's elastic modulus on the coating thickness
Elastic modulus is the engineering properties which is used to calculate the three-dimensional deformation of the coating material,load and the roll geometry. In the rubber roller coating, the changes of the rubber roller's elastic modulus will cause coating thickness changes.In equation (7) ,elasticity number Es is Es ,E denotes the effective elastic modulus of the rubber materials,and E can be expressed: Here E 1 is Young modulus, υ is poisson ratio of the rubber that covers the deformable roll. Now,we check the influence of rubber roller's elastic modulus on the coating thickness through the experimental methods. The Main experimental characteristics of the rubber roller's elastic modulus have been provided in Table 1 as shown. Choosing the different rubber rollers ,we do the experiments,the results can be seen in Fig. 5.
From Fig.5,we can see the coating thickness decreases as the elastic modulus increases,and in the area of the elastic modulus smaller, the value of coating thickness falls quickly. In equation (10),we can also see  the coating thickness and the elastic modulus reverse reduced.

Influence of rubber roller's loading force on the coating thickness
In the coating process,the external loading force on the rubber roller is through the cylinder achieved.In the mechanical structure, rubber roller and cylinder connected, the cylinder's motion changes the value of loading force.If the value of loading force is too large,the deformation of rubber roller will be too big,thus it affectsthe coating quality. If the value of loading force is too small,the rubber roller has no distortion or the clearance of the rubber roller and coating roller is too large,it also affects the coating quality.So Choosing the right loading force isvery important factors in the rubber roller coating. In equation (8)，load parameter F w =W/ER， here W is Applied load by cylinder. Now,we check the influence of rubber roller's loading force on the coating thickness through the experimental methods.The Main experimental characteristics of the rubber roller's loading force have been provided in Table  2 as shown. Change the the value of the loading force, the results can be seen in Fig.6.
From Fig.6,we can see the coating thickness decreases as the load force increases,and in the area of the load force smaller, the value of coating thickness falls slowy. In equation (10),we can also see the coating thickness and the load force reverse reduced.

Conclusions
The ideal state in actual coating production is to obtain a stable predetermined thickness coating. For the rubber roller coating system, the main factors affecting the coating thickness include roller radius, speed, coating fluid viscosity, elastic modulus of the rubber layer, and the load on the rubber roller. The elastic modulus of the rubber layer and the load on the rubber roller have an impact on the stability of the coating. To obtain a thinner coating in production, the elastic modulus of the rubber layer can be increased or the load can be increased. To avoid unacceptable vertical bar defects, the roller speed should not exceed a certain limit. By adjusting a single variable, it may be difficult to achieve an ideal state, and multiple variables need to be adjusted simultaneously. When designing a rubber roller coating system, it is necessary to consider the diameter of the roller, the range of load applied to the rubber roller, the hardness of the rubber roller, the viscosity range and speed limit of the applicable coating fluid, etc.
The above conclusion provides a direction for achieving the desired coating adjustment, but does not clarify the quantitative relationship between the coating and influencing factors. Experimental exploration is needed for the actual operating process parameters, especially for coating fluids with non Newtonian characteristics. In the future, a coating experimental platform will be established to further verify the conditions for the system to obtain a stable predetermined thickness of coating.